GATE AG 2012 • Q1 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Matrices and determinants

Question Statement:

The matrix $\begin{bmatrix} 0 & 2 & -3 \\ -2 & 0 & 4 \\ 3 & -4 & 0 \end{bmatrix}$ is:

Options:

  • (A) diagonal
  • (B) symmetric
  • (C) skew symmetric
  • (D) triangular

Official Answer Key:

C

Step-by-Step Solution & Explanation

A matrix A is skew-symmetric if a_ij = -a_ji for all i,j (and diagonal entries are zero). Here a12=2, a21=-2; a13=-3, a31=3; a23=4, a32=-4 — each off-diagonal pair is equal and opposite, and all diagonal entries are 0. Hence the matrix satisfies Aᵀ = -A. Answer: C.

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